Find a local linear approximation of f(x) = x sqrt(3 − 2x) and use it to estimate 0.99 sqrt(1.02)

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+4x−4 at x=1 using the average…

A: Consider the given function f(x)=−x2+4x−4

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Use derivatives to find two positive numbers a and b such that: a^2 +b^2 = 1 and 2a+3b is as…

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Q: Find the average rate of change of f(x) with respect to x on the interval. f(x)= x^2 -5x+1; [-3,0]

A: f(x)=x2-5x+1;-3,0 We need to find the average rate change of f(x)

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

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Q: Find the third derivative. 1 (x + y)Z + (x – y)Z = a

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Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: When is f (t) increasing at the greatest rate?

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Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: If  f '(x) = x4,  what is f(x)? (Use C for the constant of integration.)

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

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Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

A:

Q: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

A:

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: 2) Find the derivative of the function. T(r) = ar² + 2e" + n². %3D

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

A:

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: %3D 10. Find the derivative of the function )= V 5T4 using the limiting process.

A: Given,

Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Use derivatives to find two positive numbers a and b such that a^(2)+b^(2)=1 and such that 2a+3b is…

A: Solved below

Q: Let y=sin(5x)y=sin(5x). If Δx=0.1Δx=0.1 at x=0x=0, use linear approximation to estimate Δy and find…

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Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: Find a formula for n.th order derivative of the given functions. 1 b) f(x) = VT 1 a) f(x) = c) f(x)…

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Q: Use differentials to approximate the change in f(x)=x3+x2-2x+1 when x=2 and dx=0.05 a. 0.1 b. 7…

A: Use differentials to approximate the change in f(x)=x3+x2-2x+1 when x=2 and dx=0.05 a. 0.1 b. 7 c.…

Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x) =…

A: To approximate the value of the first derivative of the below function at x=2 with h=0.1. fx=xex

Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

Q: Confirm the approximations by using the linear approximation at x = 0

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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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Q: Find the third derivative of f (z) = T2x +I. fll! (z) =

A: Explanation of the answer is as follows